This paper focuses on radio resource allocation in OFDMA networks for maximizing the energy efficiency subject to the data rate requirements of users. We propose the energy-efficient water-filling structure to obtain the closed-form optimal energy-efficient power allocation for a given subcarrier assignment. Moreover, we establish a new sufficient condition for the optimal energy-efficient subcarrier assignment. Based on the theoretical analysis, we develop a joint energy-efficient resource allocation (JERA) algorithm to maximize the energy efficiency. Simulation results show that the JERA algorithm can yield optimal solution with significantly low computational complexity.